An implicit equation specifies a relation among variables without solving explicitly for one of them. An equation 
defines an implicit plane curve when its solution set
is locally one-dimensional. Where 
, the implicit
function theorem gives a local function 
.
Implicit Equation
See also
Equation, Implicit Function, Implicit Function Theorem, Plane CurveExplore with Wolfram|Alpha
References
Krantz, S. G. and Parks, H. R. The Implicit Function Theorem. Boston, MA: Birkhäuser, 2002.Cite this as:
Weisstein, Eric W. "Implicit Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ImplicitEquation.html